Research On The Fractional-order Control Scheme Of Multi-agent Systems With Time Delay

In recent years,the research of multi-agent systems has become a hot topic in the field of control science which has a wide application prospect in engineering,biology and socio-economy.With the rapid development of fractional-order control theory,fractional-order control has attracted a great number of researchers.In this thesis,a fractional-order control strategy for multi-agent systems with time delay is proposed based on control theory and fractional calculus.The multi-agent systems can get greater tracking performance and robustness.Firstly,a low-order fractional-order control scheme for multi-agent systems with time delay is proposed.A proportional(P)controller is applied to each agent with time delay in a multi-agent system.The stable region of P controller is obtained based on the generalized Nyquist stability criterion.For a multi-agent system consists of agents with double-integrator and time delay,a proportional-differential(PD)controller is designed to drive the system to achieve consensus on the basis of D-partition method.All the parameters in the region can ensure the consensus of the system.Secondly,a design method of fractional proportional-integral-differential(PID)controller for general multi-agent systems is presented.For each subsystem,the boundary of the stable region is obtained based on the D-partition method and the singular frequency method.The stable region is determined by Nyquist stability criterion.The parameter region of PID controller that drives the system to reach consensus is obtained by intersecting the stable region of each subsystem.By sweeping the control parameters in the obtained region,the fastest convergence rate can be achieved which improves the performance of the multi-agent system.When there are agents with poor performance in a multi-agent system,it is difficult to achieve good performance for the system only using distributed control scheme.In order to acquire robustness and fast convergence rate at the same time,a two-degree-of-freedom control scheme is proposed.In this control scheme,the individual controllers and the coupling controllers control the agents and their neighbors,respectively,to ensure the robustness and the fast convergence speed simultaneously.In this thesis,a fractional-order control strategy is proposed for multi-agent systems with time delay.The region of control parameters is obtained in an analytical form,which makes it more convenient to adjust the parameters.The fractional-order control scheme increases the dimension of the control parameters,allowing better performance of the multi-agent systems.